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İSTANBUL TECHNICAL UNIVERSITY INSTITUTE OF SCIENCE AND TECHNOLOGY DESIGN AND THE APPLICATION OF A CAPILLARY RHEOMETER TO THE DETERMINATION OF THE FLOW CHARACTERISTICS OF HDPE M.Sc Thesis by İsminur GÖKGÖZ Department: Polymer Science and Technology Programme: Polymer Science and Technology JANUARY 2008 İSTANBUL TECHNICAL UNIVERSITY INSTITUTE OF SCIENCE AND TECHNOLOGY DESIGN AND THE APPLICATION OF A CAPILLARY RHEOMETER TO THE DETERMINATION OF THE FLOW CHARACTERISTICS OF HDPE M.Sc Thesis by İsminur GÖKGÖZ (515041022) Date of submission : 24 December 2007 Date of defence examination: 28 January 2008 Supervisor (Chairman): Prof Dr F Seniha GÜNER Members of the Examining Committee Prof.Dr Nurseli UYANIK (İ.T.Ü.) Prof.Dr İsmail TEKE (Y.T.Ü.) JANUARY 2008 İSTANBUL TEKNİK ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ HDPE’NİN AKIŞ KARAKTERİSTİKLERİNİN BELİRLENMESİ İÇİN BİR KAPİLER REOMETRE TASARIMI VE UYGULANMASI YÜKSEK LİSANS TEZİ İsminur GÖKGÖZ (515041022) Tezin Enstitüye Verildiği Tarih : 24 Aralık 2007 Tezin Savunulduğu Tarih : 28 Ocak 2008 Tez Danışmanı : Diğer Jüri Üyeleri Prof.Dr F.Seniha GÜNER Prof.Dr Nurseli UYANIK (İ.T.Ü.) Prof.Dr İsmail TEKE (Y.T.Ü.) OCAK 2008 PREFACE Firstly, I would like to thank my adviser, Prof Dr Seniha Güner, Prof Dr Nurseli Uyanık and Dizayn Group Reseach and Technology Development department for their invaluable supports Especially, I would like to thank Dr Zafer Gemici, department manager, for always being there to encourage me and help in guiding me on some mechanical engineering problems with Prof Dr İsmail Teke I would like to thank appreciate the support offered by my friends, Sỹleyman Deveci, ĩmit Gỹler, Oktay Ylmaz, Volkan Uỗar and especially Tamer Birtane for help in technical drawing of rheometer I would like also to thank Atomika Technic Company which is distributor of Malvern Instrument, Yrd Doỗ Dr Necati ệzkan and Dr.İlhan Özen for their advices Lastly, I would like to thank my parents for their continued supports January 2008 İsminur GÖKGÖZ ii TABLE OF CONTENTS ABBREVIATIONS LIST of TABLES LIST of FIGURES LIST of SYMBOLS ÖZET SUMMARY INTRODUCTION BASIC CONCEPTS of POLYMER MELT RHEOLOGY 2.1 Shear Viscosity 2.1.1 Various types of Fluids 2.1.2 Time-dependent flow behaviour 2.2 Shear Rate-Dependent Viscosity Laws 2.2.1 Power Law 2.2.2 Bird-Carreau Law 2.2.3 Cross Law 2.2.4 Carreau-Yasuda Law 2.3 Viscosity Parameters 2.3.1 Viscosity Temperature Relationship 2.3.2 Viscosity Molecular Weight Relationship 2.3.3 Viscosity Pressure Relationship 2.4 Normal Stress 2.4.1 Normal Stress Effects SOME COMMONLY USED RHEOMETERS 3.1 Poiseuille and Couette Flows 3.1.1 Capillary Rheometer 3.1.2 Melt Flow Index 3.1.3 Rotational Rheometers 3.2 Rheometer Selection CAPILLARY RHEOMETER 4.1 Types of Capillary Rheometer 4.1.1 Controlled Shear Rate 4.1.2 Nitrogen Gas Capillary Rheometer 4.1.3 Inline/Online Capillary rheometer 4.2 Useage Areas Of Capillary Rheometer 4.2.1 Material characterization 4.2.2 Thermal Stability 4.2.3 Melt Density 4.2.4 Process Control Optimization 4.2.5 Melt Tensile Tests 4.2.6 Thermal Conductivity Measurement 4.2.7 Wall Slip Effect 4.2.8 Pressure -Viscosity Relationship 4.2.9 Die Swell Measurement EQUATIONS for SHEAR VISCOSITY MEASUREMENT iii v vi vii ix xi xii 4 8 10 10 10 11 11 13 15 15 18 21 21 22 24 27 31 33 33 33 35 36 39 39 39 40 40 40 42 44 48 50 52 5.1 Velocity profile inside the tube 5.2 Used Corrections 5.2.1 Rabinowitch Correction 5.2.2 Bagley Correction CAPILLARY RHEOMETER DESIGN 6.1 Die 6.1.1 Die Material 6.1.2 Die Size 6.2 Piston 6.2.1 Piston Lenght 6.2.2 Piston Size 6.3 Barrel 6.3.1 Barrel Material 6.3.2 Barrel Size 6.3.3 Maximum Pressure in the barrel 6.3.4 Minimum wall thickness of barrel 6.4 Operation Control Systems 6.4.1 Pressure Measurement 6.4.2 Temperature Measurement EXPERIMENTAL PART 7.1 Set Up Parameters 7.1.1 Temperature 7.1.2 Shear Range Selection 7.1.3 Min and max piston speeds 7.2 Test Material and Procedure 7.3 Capillary Rheometers Used As a Comparision Rheometry RESULTS OF CAPILLARY RHEOMETRY MEASUREMENTS 8.1 Apparent Shear Rate Values 8.2 Bagley Plots 8.3 Calculating Shear Stress 8.4 Comparision of Apparent Shear Viscosity Results for HDPE 8.5 Determine Power Law Index CONCLUSIONS REFERANCES CV iv 52 53 53 54 58 58 58 58 59 59 65 66 66 66 67 67 68 68 68 69 69 69 70 70 71 71 74 74 74 77 78 78 81 82 89 ABBREVIATIONS ASTM EPDM HDPE LDPE LLDPE MCPE MFI MFR MDPE PE PEEK PES PMMA PP UHDPE : American Society for Testing and Materials : Ethylene/propylene/diene rubber : High density polyethylene : Low density polyethlene : Lineer low density polyethylene : Metallocene catalyzed polyethylene : Melt flow index : Melt flow rate : Medium density polyethylene : Polyethylene : Polyetheretherketone : Polyether sulfone : Polymethyl methacrylate : Polypropylene : Ultra high density polyethylene v LIST of TABLES Page No Table 1.1: Rheology since its inception in 1929 Table 6.1: Allowed piston load for a material having Sy=300MPa and E=207GPa .63 Table 7.1: Standart testing temperature suggected by ASTM D 3835 69 Table 7.2: Propereties of used HDPE 71 Table 7.3: Dynisco LCR 7000 capillary rheometer .73 Table 7.4: Malvern RH 10D capillary rheometer 73 Table 7.5: Designed capillary rheometer 73 Table 8.1: Apparent shear rate values for HDPE 74 Table 8.2: Measured pressure values for L/D=5 75 Table 8.3: Measured pressure values for L/D=10 .75 Table 8.4: Measured pressure values for L/D=20 .75 Table 8.5: Measured pressure values for L/D=25 .76 Table 8.6: Linear Regression Results 76 Table 8.7: Shear stress values for HDPE 77 Table 8.8: Shear viscosity values of HDPE 79 vi LIST of FIGURES Page No Figure 2.1: Simple shear deformation Figure 2.2: Flow curves of fluids without a yield stress and with a yield stress .6 Figure 2.3: The flow curves of thixotropic and rheopexy fluid .7 Figure 2.4: Viscosity profile for a polymer melt Figure 2.5: Non-Newtonian viscosity of a LDPE melt at several different temperatures 12 Figure 2.6: The effect of molecular weight on viscosity .13 Figure 2.7: Weissenberg effect 19 Figure 2.8: Die swell 20 Figure 3.1: The Poiseuille and Couette flows .21 Figure 3.2: Schematic of a melt index 24 Figure 3.3: Comparison of the MFI to other polymer processing techniques 25 Figure 3.4: Comparison of two resins with MFI = 1.0 26 Figure 3.5: Rheological comparison of three resins 26 Figure 3.6: Schematic diagram of basic tool geometries for the rotational rheometer; (a) concentric cylinder, (b) cone and plate, (c) paralel plate 27 Figure 3.7: Cone and plate rheometer 28 Figure 3.8: Parallel plate rheometer 30 Figure 3.9:Graph of application processes and shear rates 32 Figure 4.1:Schematic diagram of a capillary extrusion rheometer 33 Figure 4.2: Slit die .34 Figure 4.3: Circular die 35 Figure 4.4: Automated nitrogen driven capillary rheometer designed as a twin bore system 36 Figure 4.5: Schematic diagram showing the principal features of a constant speed screw extrusion type capillary rheometer 36 Figure 4.6: Side stream rheometer 37 Figure 4.7: Triple bore capillary rheometer 39 Figure 4.8: Rheotens 41 Figure 4.9:Triple bore capillary rheometer 43 Figure 4.10: Thermal conductivity probe .43 Figure 4.11: Photograph of the severe melt flow instability 44 Figure 4.12: A typical flow curve of a linear polyethlene as determined by a capillary rheometer 45 Figure 4.13: Pressure fluctuations indicate melt fracture in HDPE .46 Figure 4.14: Slip at the wall in a sliding plate rheometer 47 Figure 4.15: Determine wall slip velocity 48 Figure 4.16: Scheme of modified capillary rheometer with a back pressure device .49 Figure 4.17: Scheme of modified capillary rheometer for die swell measurement 50 Figure 5.1: Pressure changing in capillar rheometer 55 Figure 5.2: Bagley plot 55 vii Figure 5.3: Problems in Bagley correction 56 Figure 5.4: Orifice die method 57 Figure 6.1: Analysis of a straight centrally loaded piston .60 Figure 6.2: End fixity coefficients of some structures 61 Figure 7.1: Dynisco LCR 7000 capillary rheometer 71 Figure 7.2: Malvern RH 10D capillary rheometer 72 Figure 7.3: Designed capillary rheometer 72 Figure 8.1: Comparing the Bagley plots .76 Figure 8.2: Comparison of apparent shear viscosity results 78 Figure 8.3: Plot of the ln ( τ w ) versus ln ( γ ) for HDPE at 190°C 79 Figure 8.4: Flow curve of HDPE at 190°C 80 • a viii L/D=5 Table 8.2: Measured pressure values for L/D=5 Plunger Speed (mm/min) Measured Pressure (Bar) 18.3 78 9.41 62 4.83 49 2.48 39 1.27 30 0.66 23 L/D=10 Table 8.3: Measured pressure values for L/D=10 Plunger Speed (mm/min) Measured Pressure (Bar) 18.3 118 9.41 95 4.83 74 2.48 62 1.27 49 0.66 37 L/D=20 Table 8.4: Measured pressure values for L/D=20 Plunger Speed (mm/min) Measured Pressure (Bar) 18.3 230 9.41 188 4.83 153 2.48 122 1.27 95 0.66 75 75 L/D=25 Table 8.5: Measured pressure values for L/D=25 Plunger Speed (mm/min) Measured Pressure (Bar) 18.3 276 9.41 226 4.83 182 2.48 145 1.27 115 0.66 88 Measured Pressure (Bar) 300 250 200 150 100 50 0 10 15 20 L/D Figure 8.1: Comparing the Bagley plots Linear regression analysis results are given in Table 8.6 Table 8.6: Linear Regression Results Shear Rate (1/s) R² 19.8 38.1 74.4 144.9 282.3 549 0.995 0.998 0.997 0.994 0.996 0.997 76 25 30 As seen in Figure 8.1, pressure increases with increasing shear rate and L/D ratio This result is expected because according to Equation 5.5, the pressure drop is correlated to the shear stress and L/D ratio of capillary and according to the Power law, shear stress is depend on shear rate values Thefore shear stress increase with increasing shear rate The similar results are given in literature [33, 88] 8.3 Calculating Shear Stress Shear stress values were calculated with Equation 5.5 and Table 8.6 shows these results Table 8.7: Shear stress values for HDPE Shear Rate (1/s) 549 282.3 144.9 74.4 38.1 19.8 L/D 10 20 25 10 20 25 10 20 25 10 20 25 10 20 25 10 20 25 Measured pressure (Bar) Average Shear ∆Pend (Bar) (∆Ptot) Stress (Pa) 78 118 23.1 255818.8 230 276 62 95 16.45 212028.1 188 226 49 77 11.05 173565.6 153 184 39 62 10.4 136525 122 145 30 49 7.45 108403.1 95 115 23 37 5.35 84271.88 75 88 77 8.4 Comparision of Apparent Shear Viscosity Results for HDPE Figure 8.2 shows comparision of experimental results which gained from the capillary rheometers used As can be seen, good agreement between results is obtained Shear Viscosity (Pa.s) 10000 1000 100 10 100 1000 Shear Rate (1/s) DESIGNED RHEOMETER ODTU SABANCI UNIVERSITY Figure 8.2: Comparison of apparent shear viscosity results 8.5 Determine Power Law Index In order to determine true the shear rate, the slope should be find by plotting the ln(τ w ) versus the ln( γ a ) as shown in Figure 8.3 • As known polyethylene melts, like many other polymeric materials, deviate from ideal Newtonian behavior The corrected shear viscosity of HDPE ,η , can be calculated using Equation 5.10 which is the shear stress divided by the actual shear rate Table 8.7 shows shear viscosity data and Figure 8.4 shows flow curve of HDPE 78 • Figure 8.3: Plot of the ln (τ w ) versus ln ( γ a ) for HDPE at 190°C Table 8.8: Shear viscosity values of HDPE Apparent Power Law Corrected Shear Corrected Shear Index (n) Rate (1/s) Viscosity (Pa.s) 549 0.33 827.34 309.21 282.3 0.33 425.43 498.39 144.9 0.33 218.36 794.84 74.4 0.33 112.12 1217.66 38.1 0.33 57.42 1888.01 19.8 0.33 29.84 2824.26 Shear Rate HDPE (1/s) 79 Shear Viscosity (Pa.s) 10000 1000 100 10 10 100 Shear Rate (1/s) Figure 8.4: Flow curve of HDPE at 190°C 80 1000 CONCLUSIONS In this study, a simple capillary rheometer was designed according to the ASTM standards As a part of the rheometer a tensile testing machine was attached for the push and pull movements The rheometer was tested with HDPE using three different dies and the results were compared with those of the rheometers which are produced by Malvern and Dynisco Instruments The operation temperature was adjusted 190°C The rheometer designed in this study gave the similar results with the commercial rheometers used As a view of design parameters, the main difference is that requiring force is generated by a tensile testing machine in the rheometer developed in this study For this reason, the cost for producing it is lower than that of commercial rheometer The importance of this study is that a scientific study was done and published about rheometer design due to there is only patent publications in literature In the future, the data for solving some processing problems such as melt fracture or die swell can be obtained by using capillary rheometer designed and the effects of some parameters such as temperature, pressure and, type and amount of additives on rheological behavior can be determined So, obtained data can be used for improving the process conditions Additionally, software can be written to make the calculations easily and a twin bore capillary rheometer can be designed for doing the tests in a short time 81 REFERENCES [1] Morrison, F.A., 2004 What is rheology anyway?, The Industrial Physicist, 10(2), pp 29-31 [2] Doraiswamy, D., 2001 The origins of rheology: a short of historical 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